A New Method for m-sequence and Gold-sequence Generator Polynomial Estimation

A finite field discrete Fourier transform is used for studying the properties of linear feedback shift register (LFSR) sequence with period (q
¹
-1)/n, and the elation of sequence' s linear complexity and the nonzero-points in frequency-domain is given in this paper. Then a new algorithm is introduced to estimate the generator polynomial and initial state of m-sequence and gold-sequence. Based on the principle of FFT, a fast algorithm is also explored.